Dimension and sampling of the near-field and its intensity over curves

The paper addresses the question of efficiently sampling the near field and its intensity over an arbitrary curved line. It aims at finding the minimum number of measurements and their position for discretizing the near field and its square amplitude without loss of information and follows a common approach for both the radiation operator and the correspondent lifting operator. A scalar geometry is examined for both electric and magnetic current sources. At first, the singular values of the radiation / lifting operator are evaluated by an asymptotic approach and a change of variables which lead to an operator with a widely investigated spectrum. As the number of relevant singular values is available in closed form, the dimensions of the near field and its intensity over the curve are found. Next, starting from a sampling expansion of the pertinent left singular functions, a non-redundant sampling representation of the near field and its square amplitude is provided. Some numerical results confirm the analysis. The results may be of great interest especially in antenna testing by near field data (both standard and phaseless) with an unconventional field scanning system as, for instance, an UAV mounted probe.